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Thermal Noise (  100Hz) What happens if we perform the following measurement? Time SeriesFrequency Spectrum Spectrum Analyser R

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Thermal Noise (  100Hz) The resistor has a mean-square voltage noise (  130nV/  Hz for 1M  ) called Johnson or Brownian noise. This is a white noise. The fluctuating voltage is due to the dissipation in the resistor and can be described by the fluctuation dissipation theorem: The response of a system in thermodynamic equilibrium to a small applied force is the same as its response to a spontaneous fluctuation. A mechanical system with dissipation has a mean-square fluctuating force noise b

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Thermal Noise (  100Hz) Z is the mechanical impedance (the real part is equivalent to resistance in our electrical analogy) In terms of displacement the thermal noise is given by: It is convenient to introduce the loss (  ) into the spring constant and the displacement noise is (for  f=1Hz)

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Thermal Noise (  100Hz) The impedance then becomes or and the displacement noise is The shape of the thermal noise spectrum depends on the type of damping (external velocity) or friction (internal).